An oil immersion microscope can just resolve two point objects separated by 0.6 m, when light of wavelength 485 nm is used for illumination. If the semi vertical angle is `20^@`, calculate the refractive index of the oil used and resolving power of the microscope.

Explanation

`lamda=485 mm=485 times10^-9 m`
`dx=0.6 times10^-6 m, theta=20^@, n=?` resolving power
We have `dx=(1.22 lamda)/(2 n sin theta)`
`n=(1.22 lamda)/(2d times sin theta)=(1.22 times 485 times 10^-9)/(2 times0.6 times10^-6 times sin20^@)`
`=(1.22 times 485 times 10^-9)/(2 times0.6 times10^-6 times 0.342)=1.44`
Resolving power =`1/(dx)=1/(0.6 times10^-6)=1.66 times10^6`
Result: Refraction index of the oil speed= 1.44 ,
Resolving power of the microscope =`1.66 times 10^6`.